This paper main goal is to introduce the basic language and programming styles of the mathematical software Mathematica (5.2), and applies it to solve problems in algebra, calculus, linear algebra, probability and statistics. We hope readers can enhance the interest of learning mathematics by the aid of software, verify the common theorem using the software, and solving mathematical problems.

A bigraph-driven vending machine is implemented. The application is realized as a Spring-based webservice. Actions can be initiated by REST endpoints. The system follows a rule-based architecture, where possible operations are grounded on a rule set. Bigraphical Reactive Systems are used for the specification and execution. The actual state of the application is a bigraph stored in a database, which can be viewed and altered directly in the database. A history of states is kept - the application can be transferred to any prior state. The application can be updated or extended by merely changing the bigraphical database model.:First Part: A system of a vending machine is specified and analyzed using BDSL. This concerns the static and dynamic aspects of the system. Second Part: The analysis results are re-used for the implementation using Bigraph Framework. The application is realized as a webservice that is built using the Spring framework. / Ein bigraph-gesteuerter Verkaufsautomat wird implementiert. Die Anwendung ist als Spring-basierter Webservice realisiert. Aktionen können über REST-Endpunkte initiiert werden. Das System folgt einer regelbasierten Architektur, bei der die möglichen Operationen auf einem Regelsatz beruhen. Für die Spezifikation und Ausführung werden Bigraphical Reactive Systems verwendet. Der aktuelle Zustand der Anwendung ist ein in einer Datenbank gespeicherter Bigraph, der direkt in der Datenbank eingesehen und verändert werden kann. Es wird eine Historie der Zustände geführt - die Anwendung kann in einen beliebigen früheren Zustand überführt werden. Die Anwendung kann aktualisiert oder erweitert werden, indem lediglich das bigraphische Datenbankmodell geändert wird.:First Part: A system of a vending machine is specified and analyzed using BDSL. This concerns the static and dynamic aspects of the system. Second Part: The analysis results are re-used for the implementation using Bigraph Framework. The application is realized as a webservice that is built using the Spring framework.

Context-aware pervasive computing has attracted a significant research interest from both academy and industry worldwide. It covers a broad range of applications that support many manufacturing and daily life activities. For instance, industrial robots detect the changes of the working environment in the factory to adapt their operations to the requirements. Automotive control systems may observe other vehicles, detect obstacles, and monitor the essence level or the air quality in order to warn the drivers in case of emergency. Another example is power-aware embedded systems that need to work based on current power/energy availability since power consumption is an important issue. Those kinds of systems can also be considered as smart applications. In practice, successful implementation and deployment of context-aware systems depend on the mechanism to recognize and react to variabilities happening in the environment. In other words, we need a well-defined and efficient adaptation approach so that the systems' behavior can be dynamically customized at runtime. Moreover, concurrency should be exploited to improve the performance and responsiveness of the systems. All those requirements, along with the need for safety, dependability, and reliability pose a big challenge for developers.In this thesis, we propose a novel programming language called INI, which supports both event-based and rule-based programming paradigms and is suitable for building concurrent and context-aware reactive applications. In our language, both events and rules can be defined explicitly, in a stand-alone way or in combination. Events in INI run in parallel (synchronously or asynchronously) in order to handle multiple tasks concurrently and may trigger the actions defined in rules. Besides, events can interact with the execution environment to adjust their behavior if necessary and respond to unpredictable changes. We apply INI in both academic and industrial case studies, namely an object tracking program running on the humanoid robot Nao and a M2M gateway. This demonstrates the soundness of our approach as well as INI's capabilities for constructing context-aware systems. Additionally, since context-aware programs are wide applicable and more complex than regular ones, this poses a higher demand for quality assurance with those kinds of applications. Therefore, we formalize several aspects of INI, including its type system and operational semantics. Furthermore, we develop a tool called INICheck, which can convert a significant subset of INI to Promela, the input modeling language of the model checker SPIN. Hence, SPIN can be applied to verify properties or constraints that need to be satisfied by INI programs. Our tool allows the programmers to have insurance on their code and its behavior.

Les applications réactives et sensibles au contexte sont des applications intelligentes qui observent l’environnement (ou contexte) dans lequel elles s’exécutent et qui adaptent, si nécessaire, leur comportement en cas de changements dans ce contexte, ou afin de satisfaire les besoins ou d'anticiper les intentions des utilisateurs. La recherche dans ce domaine suscite un intérêt considérable tant de la part des académiques que des industriels. Les domaines d'applications sont nombreux: robots industriels qui peuvent détecter les changements dans l'environnement de travail de l'usine pour adapter leurs opérations; systèmes de contrôle automobiles pour observer d'autres véhicules, détecter les obstacles, ou surveiller le niveau d'essence ou de la qualité de l'air afin d'avertir les conducteurs en cas d'urgence; systèmes embarqués monitorant la puissance énergétique disponible et modifiant la consommation en conséquence. Dans la pratique, le succès de la mise en œuvre et du déploiement de systèmes sensibles au contexte dépend principalement du mécanisme de reconnaissance et de réaction aux variations de l'environnement. En d'autres termes, il est nécessaire d'avoir une approche adaptative bien définie et efficace de sorte que le comportement des systèmes peut être modifié dynamiquement à l'exécution. En outre, la concurrence devrait être exploitée pour améliorer les performances et la réactivité des systèmes. Tous ces exigences, ainsi que les besoins en sécurité et fiabilité constituent un grand défi pour les développeurs.C’est pour permettre une écriture plus intuitive et directe d'applications réactives et sensibles au contexte que nous avons développé dans cette thèse un nouveau langage appelé INI. Pour observer les changements dans le contexte et y réagir, INI s’appuie sur deux paradigmes : la programmation événementielle et la programmation à base de règles. Événements et règles peuvent être définis en INI de manière indépendante ou en combinaison. En outre, les événements peuvent être reconfigurésdynamiquement au cours de l’exécution. Un autre avantage d’INI est qu’il supporte laconcurrence afin de gérer plusieurs tâches en parallèle et ainsi améliorer les performances et la réactivité des programmes. Nous avons utilisé INI dans deux études de cas : une passerelle M2M multimédia et un programme de suivi d’objet pour le robot humanoïde Nao. Enfin, afin d’augmenter la fiabilité des programmes écrits en INI, un système de typage fort a été développé, et la sémantique opérationnelle d’INI a été entièrement définie. Nous avons en outre développé un outil appelé INICheck qui permet de convertir automatiquement un sous-ensemble d’INI vers Promela pour permettre un analyse par model checking à l’aide de l’interpréteur SPIN. / Context-aware pervasive computing has attracted a significant research interest from both academy and industry worldwide. It covers a broad range of applications that support many manufacturing and daily life activities. For instance, industrial robots detect the changes of the working environment in the factory to adapt their operations to the requirements. Automotive control systems may observe other vehicles, detect obstacles, and monitor the essence level or the air quality in order to warn the drivers in case of emergency. Another example is power-aware embedded systems that need to work based on current power/energy availability since power consumption is an important issue. Those kinds of systems can also be considered as smart applications. In practice, successful implementation and deployment of context-aware systems depend on the mechanism to recognize and react to variabilities happening in the environment. In other words, we need a well-defined and efficient adaptation approach so that the systems' behavior can be dynamically customized at runtime. Moreover, concurrency should be exploited to improve the performance and responsiveness of the systems. All those requirements, along with the need for safety, dependability, and reliability pose a big challenge for developers.In this thesis, we propose a novel programming language called INI, which supports both event-based and rule-based programming paradigms and is suitable for building concurrent and context-aware reactive applications. In our language, both events and rules can be defined explicitly, in a stand-alone way or in combination. Events in INI run in parallel (synchronously or asynchronously) in order to handle multiple tasks concurrently and may trigger the actions defined in rules. Besides, events can interact with the execution environment to adjust their behavior if necessary and respond to unpredictable changes. We apply INI in both academic and industrial case studies, namely an object tracking program running on the humanoid robot Nao and a M2M gateway. This demonstrates the soundness of our approach as well as INI's capabilities for constructing context-aware systems. Additionally, since context-aware programs are wide applicable and more complex than regular ones, this poses a higher demand for quality assurance with those kinds of applications. Therefore, we formalize several aspects of INI, including its type system and operational semantics. Furthermore, we develop a tool called INICheck, which can convert a significant subset of INI to Promela, the input modeling language of the model checker SPIN. Hence, SPIN can be applied to verify properties or constraints that need to be satisfied by INI programs. Our tool allows the programmers to have insurance on their code and its behavior.